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From Atomistic to Continuum Descriptions of Morphological Evolution

Published online by Cambridge University Press:  01 February 2011

Christoph A. Haselwandter and
Dimitri D. Vvedensky
Christoph A. Haselwandter
Affiliation:
The Blackett Laboratory, Imperial College, London, SW7 2BW, United Kingdom
Dimitri D. Vvedensky
Affiliation:
The Blackett Laboratory, Imperial College, London, SW7 2BW, United Kingdom
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Abstract

Lattice Langevin equations are derived from the rules of lattice growth models. These provide an exact mathematical description that is suitable for direct analysis, such as the passage to the continuum limit, as well as a computational alternative to kinetic Monte Carlo simulations. This approach is applied to ballistic deposition and a model for conditional deposition, both of which yield the Kardar–Parisi– Zhang equation in the continuum limit, and a model of strain relaxation during heteroepitaxy.

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